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A theory of stacks with twisted fields and resolution of moduli of genus two stable maps

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arxiv 2005.03384 v3 pith:KFYRNOZR submitted 2020-05-07 math.AG

Yi Hu , Jingchen Niu This is my paper
classification math.AG
keywords genusmapsmodulistablefieldstheorytwistedarticle
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We construct a smooth algebraic stack of tuples consisting of genus two nodal curves, simple effective divisors away from the nodes, and twisted fields. It provides a desingularization of the moduli of genus two stable maps to projective spaces. The construction is based on systematic application of the theory of stacks with twisted fields (STF), which has its prototype appeared in arXiv:1201.2427 and arXiv:1906.10527 and is fully developed in this article. As a byproduct of the STF theory, we also obtain a novel desingularization of the moduli of genus one stable maps to projective spaces, which is isomorphic to the blowup that reverses the order used by Vakil-Zinger and Hu-Li. The results of this article are the second step of a program toward the resolutions of the moduli of stable maps of higher genera.

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Cited by 3 Pith papers

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  1. Reduced Gromov-Witten invariants without ghost bubble censorship

    math.SG 2026-04 unverdicted novelty 7.0 of 10

    Defines all-genus reduced Gromov-Witten invariants of symplectic manifolds via effectively supported multivalued perturbations on derived orbifold/Kuranishi charts, bypassing ghost bubble censorship.

  2. Reduced Gromov-Witten invariants without ghost bubble censorship

    math.SG 2026-04 conditional novelty 7.0 of 10

    All-genus reduced Gromov–Witten invariants are defined for compact symplectic manifolds via normally complex stratified multisections on Kuranishi atlases.

  3. Higher genus reduced Gromov--Witten invariants via desingularizations of sheaves

    math.AG 2023-10 unverdicted novelty 5.0 of 10

    Two desingularization constructions for coherent sheaves on stacks are used to define reduced Gromov-Witten invariants of GIT quotients in higher genera.

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